Dielectric Characterization and Separation Optimization of Inﬁltrating Ductal Adenocarcinoma Via Insulator-Dielectrophoresis

micromachines

Article Dielectric Characterization and Separation Optimization of Inﬁltrating Ductal Adenocarcinoma via Insulator-Dielectrophoresis

Ezekiel O. Adekanmbi, Anthony T. Giduthuri and Soumya K. Srivastava *

Department of Chemical and Materials Engineering, University of Idaho, Moscow, ID 83844-1021, USA; [email protected] (E.O.A.); [email protected] (A.T.G.) * Correspondence: [email protected]; Tel.: +1-208-885-7652

Received: 25 February 2020; Accepted: 23 March 2020; Published: 25 March 2020

Abstract: The dielectrophoretic separation of infiltrating ductal adenocarcinoma cells (ADCs) from isolated peripheral blood mononuclear cells (PBMCs) in a ~1.4 mm long Y-shaped microfluidic channel with semi-circular insulating constrictions is numerically investigated. In this work, ADCs (breast cancer cells) and PBMCs’ electrophysiological properties were iteratively extracted through the fitting of a single-shell model with the frequency-conductivity data obtained from AC microwell experiments. In the numerical computation, the gradient of the electric field required to generate the necessary dielectrophoretic force within the constriction zone was provided through the application of electric potential across the whole fluidic channel. By adjusting the difference in potentials between the global inlet and outlet of the fluidic device, the minimum (effective) potential difference with the optimum particle transmission probability for ADCs was found. The radius of the semi-circular constrictions at which the effective potential difference was swept to obtain the optimum constriction size was also obtained. Independent particle discretization analysis was also conducted to underscore the accuracy of the numerical solution. The numerical results, which were obtained by the integration of fluid flow, electric current, and particle tracing module in COMSOL v5.3, reveal that PBMCs can be maximally separated from ADCs using a DC power source of 50 V. The article also discusses recirculation or wake formation behavior at high DC voltages (>100 V) even when sorting of cells are achieved. This result is the first step towards the production of a supplementary or confirmatory test device to detect early breast cancer non-invasively.

Keywords: dielectrophoresis; electrophysiological properties; crossover frequency; wake or recirculation formation; dielectric spectra

1. Introduction Noncommunicable diseases (NCDs) kill more than 36 million people annually representing 63% of global deaths [1]. Breast cancer, a subset of NCDs, accounts for over 500,000 of these deaths [2] with an incidence of about 1.1 million new cases being reported per year [3]. In the United States, as of March 2017, more than 3.1 million women with a history of breast cancer has been reported [4]. About 85% of these breast cancers occur in women who have no family history of breast cancer [4] and one in eight women develop breast cancer in her lifetime. As of now, the main cause of breast cancer cannot be pinned down exactly, but scientists have hypothesized where breast cancer originates. Our bodies consist of many cells, which can be replaced as they age. Old cells tend to copy their DNA before splitting into new ones. However, the copying process could cause mutation which may result in cellular abnormalities called tumors. When tumor cells grow and invade neighboring tissues, they are termed cancerous [5,6]. Breast cancer that starts in the cells of the glands are termed adenocarcinoma

Micromachines 2020, 11, 340; doi:10.3390/mi11040340 www.mdpi.com/journal/micromachines Micromachines 2020, 11, 340 2 of 19

(ADCs), which can be invasive ductal (indicates that the cancer cells present in the milk ducts (Ductal Carcinoma in-situ)) and can begin to infiltrate and replace the normal surrounding tissues of the duct walls (accounts for 80% of breast cancer), also known as invasive lobular. According to the National Cancer Institute, around 90% of breast cancers are adenocarcinomas. If untreated, breast cancers can grow bigger, taking over more surrounding breast tissue. When breast cancer cells break away from the original cancer, they can enter the blood or lymph vessels. Traveling through these vessels, cancer cells may settle in other areas of the breast or in the lymph nodes of the breast tissue, forming new tumors. This is called metastasis. These adenocarcinomas are the most difficult tumor to accurately identify the primary site [7]. Diagnosis of adenocarcinoma is achieved by examining features such as tubular myelin, intranuclear surface apoprotein tubular inclusions, Langerhans cells associated with neoplastic cells, cytoplasmic hyaline globules, glycogen, lipid droplets, and cytoplasmic crystals. The diagnostic is painful since a tissue biopsy is utilized to extract the different types of cells mentioned above making it a cumbersome, time consuming, and costly process since they are ultrastructural features that are needed to be observed through electron microscopes. Another technique to diagnose adenocarcinoma is through the application of immunohistochemistry that has also been explored using estrogen and progesterone receptor proteins, thyroid transcription factor-I and surfactant apoproteins [7]. However, specificity and sensitivity are the main issues associated with this method. An alternative technique including a less invasive route is desirable to address some of the drawbacks of the current diagnostic tools used such that it is rapid, easy-to-use, economical, and sensitive. The combination of peripheral blood mononuclear cells (PBMCs) and microfluidics makes an excellent alternative that is explored through this article. In this article, we explore the use of PBMCs to detect these cancerous cells since they are known to circulate in the peripheral blood of patients, especially when breast cancer is spread beyond the ducts into other parts of the breast tissues or other organs through blood [8]. PBMCs are typically isolated from whole blood using density gradient centrifugation commonly in Ficoll-Pacque PLUS and the Histopaque 1077 media [9]. To discriminate and subsequently separate ADCs from PBMCs, increased interests have been rooted in exploring the utilization of the cell physical properties in lieu of other methods including antibody-conjugation, which is time consuming and can impact ADCs’ properties and viability [10]. Leveraging physical characteristics in the form of size-based filtration [11–13], density-gradient separation [14–16], and inertial-hydrodynamic discrimination [17–19] has been explored in the past until Shim et al. reported that size and density distributions of ADCs tend to overlap with those of PBMCs, leading to occasional inefficiency in the separation of ADCs based on size and density. An alternative technique is to utilize the electrophysiological property differences between PBMCs and ADCs in a microfluidic device, termed as dielectrophoresis (DEP). Dielectrophoresis (DEP), a microfluidic and an electrokinetic technique that could be utilized to detect ADCs from a heterogenous population of PBMCs, utilizes electric signatures like cell capacitance and conductance in a non-uniform electric gradient, and seems to be a novel alternative [20–25]. DEP is a promising technique that is utilized to characterize and manipulate different types of cells like red blood cells, bacteria, virus, yeast, and proteins. It also is capable of detecting subtle changes on the cells based on their state, i.e., alive and dead, healthy and infected. In this article we choose to characterize PBMCs and ADCs utilizing DEP as a detection tool via quantifying the unhealthy or diseased cells, i.e., cancer cells because it employs no moving parts, it is non-destructive for the bioparticles, and utilizes low electric current on a micro-chip without the need of antibody tagging or fluorescent labels making it a portable system. Reduced response time and higher throughput and accuracy makes DEP a promising technique for cancer cell detection. When a bioparticle is subjected to a non-uniform electric field, the dielectrophoretic forces and the dipole-dipole forces between the particles (dipole moments) are generated based on the differences between the electrical properties (capacitance and conductance) of cells and the surrounding fluid [23]. Traditionally, DEP based cancer cell separations employ metallic electrodes to capture infected cells, Micromachines 2020, 11, 340 3 of 19 byMicromachines creating 20 non-uniform20, 11, x electric fields using AC voltage [16,25]. AC DEP device offers a major3 of 19 disadvantage in the form of decreased metal electrode functionality due to fouling when biological associated with the fabrication containing metal parts [24,27]. To address the challenges posed by AC samples are manipulated [24,26]. Also, these devices often have high cost associated with the fabrication DEP device, we chose to explore DC electric current (insulator-based DEP (iDEP)) as an alternative containing metal parts [24,27]. To address the challenges posed by AC DEP device, we chose to to electrode-based DEP. iDEP employs insulating objects or structures created by microfabrication explore DC electric current (insulator-based DEP (iDEP)) as an alternative to electrode-based DEP. embedded in the channel to generate spatial non-uniformities in the field [28,29]. With the electrodes iDEP employs insulating objects or structures created by microfabrication embedded in the channel to placed in the inlet and outlets, here electroosmotic forces can be utilized for inducing flows, generate spatial non-uniformities in the field [28,29]. With the electrodes placed in the inlet and outlets, eliminating the need for the pumps for continuous operation [30]. The aim of this work, therefore, is here electroosmotic forces can be utilized for inducing flows, eliminating the need for the pumps for to determine experimentally if there are differences in the electrophysiological properties of normal continuous operation [30]. The aim of this work, therefore, is to determine experimentally if there PBMCs and ADCs and to use these differences, if they exist, to numerically attempt their detection are differences in the electrophysiological properties of normal PBMCs and ADCs and to use these (using DC signals) on a microchip—an important step towards the development of a supplementary differences, if they exist, to numerically attempt their detection (using DC signals) on a microchip—an diagnostic device for ADCs. important step towards the development of a supplementary diagnostic device for ADCs. In this article, we develop an in silico based COMSOL Multiphysics model for continuously In this article, we develop an in silico based COMSOL Multiphysics model for continuously detecting ADCs from a heterogenous population of PBMCs in a microchannel with modified detecting ADCs from a heterogenous population of PBMCs in a microchannel with modified geometry. geometry. To create non-uniformity in the electric field, an array of semi-circular insulating obstacles To create non-uniformity in the electric field, an array of semi-circular insulating obstacles are embedded are embedded in the microchannel. First, a PDMS-based microwell was constructed to house a in the microchannel. First, a PDMS-based microwell was constructed to house a horizontally arranged horizontally arranged 100 µm apart platinum electrode (Figure 1) to obtain the characteristic 100 µm apart platinum electrode (Figure1) to obtain the characteristic membrane properties of both membrane properties of both ADCs and PBMCs. The properties, validated against the available data ADCs and PBMCs. The properties, validated against the available data in the literature, are then in the literature, are then utilized to in conjunction with Finite Element Method (FEM) to model and utilized to in conjunction with Finite Element Method (FEM) to model and simulate the trajectory of simulate the trajectory of both cells (ADCs and PBMCs) in a semicircular-insulator-based 2D both cells (ADCs and PBMCs) in a semicircular-insulator-based 2D microfluidic channel. While the microfluidic channel. While the characterization of the ADCs gives the innate electrical signatures characterization of the ADCs gives the innate electrical signatures that is characteristic of moderately that is characteristic of moderately differentiated infiltrating ductal adenocarcinoma, the utilization differentiated infiltrating ductal adenocarcinoma, the utilization of FEM sets a workable model that of FEM sets a workable model that could serve as a platform for fabricating a novel diagnostic device could serve as a platform for fabricating a novel diagnostic device for ADCs. for ADCs.

Figure 1. 1.The The experimental experimental set-up set- forup the for measurement the measurement of dielectrophoresis of dielectrophoresis (DEP) crossover (DEP) frequencycrossover usingfrequency a novel using microwell a novel platform microwell to obtain platform electrophysiological to obtain electrophysiological properties, i.e., conductivity properties, andi.e., permittivityconductivity of and peripheral permittivity blood of mononuclear peripheral blood cell (PBMCs) mononuclear and adenocarcinoma cell (PBMCs) cellsand adenocarcinoma (ADCs) that will aidcells in (ADCs) designing that an will early aid detectionin designing platform an early for detection breast cancer. platform for breast cancer.

2. Theory of Dielectrophoresis Crossover frequency measurement is a novel dielectrophoretic-baseddielectrophoretic-based method of characterizingcharacterizing the dielectric properties of many biological particles. By By crossover crossover frequency, frequency, we mean the frequency at which cells suspended in a microwellmicrowell in anan osmotic concentration medium, change their direction of motion towards or away from the high ﬁeldfield region in an electric-ﬁeld-gradient-basedelectric-field-gradient-based system. WhenWhen a bioparticle (i.e. (i.e.,, cell) cell) is is placed placed between between the the two two elect electrodesrodes as asshown shown in Figure in Figure 1, the1, the cell cell can caneither either move move to A or to B A depending or B depending on its polarizability on its polarizability relative to relative the medium to the in medium which it inis suspended. which it is Cells move to A (pDEP) if they are more polarizable than the medium and to B (nDEP) if the reverse occurs. At varying conductivity of the suspending medium, various crossover frequency data (fxo) can be generated. In this current work, these data are generated, plotted and fitted with a model (Equation (1)) using least square regression and the confidence of the fit was found through the

Micromachines 2020, 11, 340 4 of 19 suspended. Cells move to A (pDEP) if they are more polarizable than the medium and to B (nDEP) if the reverse occurs. At varying conductivity of the suspending medium, various crossover frequency data (f xo) can be generated. In this current work, these data are generated, plotted and fitted with a model (Equation (1)) using least square regression and the confidence of the fit was found through the coefficient of regression analysis. A voltage drop at the electrode boundary is considered to be significant at frequencies below 15 kHz [30]. Also, because the reservoirs of microdevice are typically considered as an enormous source of ions compared with the microchannels themselves, any voltage drop can be neglected between the electrode and the inlet or outlet to the microchannel. In this study, the operating conditions for the crossover frequency quantification are maintained above the reported threshold and thus can neglect the voltage drop at the boundary of the electrodes that are placed in the inlet and outlet reservoirs. According to Pethig [31] or a biological cell whose interfacial polarization between the plasma membrane and the cytoplasm results in a dispersion frequency far below 1 MHz for the cell effective dielectric permittivity and conductivity, the first crossover frequency, f xo1, of the cell membrane is given by:

. fxo1 = fxo1(Cmem, Gmem, σm). q 2 (1) 1 σm RGmem RGmem fxo1 = 1 2 √2 πRCmem − 2σm − 2σm

Cmem = εmem/d (2) ∀ Gmem = σmem/d (3)

In terms of total particles and medium properties, fxo1 can also be represented as

 1/2 1  σm σp σp + 2σm  f =  −  (4) xo1   2π εp εm εp + εm  − where, Cmem is the specific membrane capacitance, Gmem the membrane conductance, σm the conductivity of the suspending medium, εmem the permittivity of the membrane, σmem the conductivity of the membrane, d is the characteristic dimension of the cell membrane and R, the radius of the particle. In → an iDEP system, the DEP force, F DEP, acting on the particles due to the field gradient is a function of the particle and medium characteristics and is given as: ! σ σ 2 → 3 p m → F DEP = 2πεmr − EDC (5) σp + 2σm ∇ σp σm where the quantity − is the Clausius-Mossotti factor (CM), which is the parameter that determines σp+2σm 2 → → whether F will be positive (as in pDEP) or negative (as in nDEP) and EDC is the field distribution DEP ∇ parameter that enhances particle polarization and dielectrophoretic separation effect. This force is usually balanced with the viscous drag within the fluid system. Prior to the utilization of DEP-viscous force balance for particle separation, electrokinetic forces (electroosmotic and electrophoretic forces) would have been utilized to pump the particles to the separation region through the electroosmotic channel wall condition and the electrostatic interaction of the electric field with the particles. Electroosmotic flow is generated due to the action of the electric field on charged interior surfaces having electrical double-layer (EDL). For the microscale flow, surface charge generated at the solid wall-ionic liquid interface is a significant interfacial property to affect the flow. This is because the surface charge at the solid–liquid interface can redistribute the charged ions in the ionic liquid and forms the electrical double layer (EDL) with local net charge density. However, because of the characteristic Micromachines 2020, 11, 340 5 of 19 length of the EDL known as Debye length is small and has the typical values from several nanometers to one micrometer (significantly small compared to the dimensions of the channel), thus the effect of EDL on the microscale flow is usually neglectable and it can only produce obvious effect on the nanoscale fluid flow. When an external electric field is applied on the ionic liquid with EDL within a microchannel, the liquid will be driven by the electric field and form the electroosmotic flow (EOF), which is a typical fluidic transport phenomenon over the microscale [32,33]. The nature and magnitude of the charge in EDL is characterized by the Zeta potential [34]. Electroosmotic mobility of fluid is a function of the Zeta potential of the microdevice, i.e., microchannel construction material and is given by [35]: ξεm µ = − (6) EO η where, µEO is the electroosmotic mobility,εm is the permittivity of medium, ξ is the Zeta potential of the material and η is the viscosity of suspending medium (buffer). The electrophoretic mobility unlike the electroosmotic mobility that depends on the material, depends on the Zeta potential of the particle itself and is given by [36]: ξpεm µ = (7) EO η where, ξp is the Zeta potential of the particle. At the separation region, the particle experiences a dielectrophoretic force that is impacted by the particle mobility. The DEP mobility is a function of CM factor and for a spherical particle it is expressed as [37]:

2 πdpεm µ = CM (8) DEP 12η where, dp is the particle diameter and η is the medium viscosity.

3. Materials and Methods

3.1. Microwell Fabrication Silicone elastomer mixed with its curing agent in 10:1 ratio (Sylgard 184, Dow Corning, Midland, MI, USA) was placed in a desiccator chamber under 0.27-mTorr vacuum in order to remove the bubbles formed during the mixing process. After three successive degassing operations lasting for 15 min, at an interval of 5 min between each run, the clear PDMS was poured into a clean petri dish and cured in the oven at 70 C for 1 h. This step was followed by dicing the PDMS into 1” 1” squares. A ◦ × 3-mm hole was punched into each of the diced PDMS to create a well onto which the cell suspension was pipetted. Scotch tape was used to remove any dirt/dust from the PDMS after which it is was irreversibly sealed to a borosilicate glass slide through plasma oxidation of 50 W RF power for 1 min. High purity platinum wire was connected to the microwell as shown in Figure1. With the aid of an Olympus IX71 inverted microscope (Olympus, Tokyo, Japan), the distance (100 µm) between the electrode tips was set. Loctite’s self-mix epoxy was used to keep the electrode spacing intact. The epoxy also prevented any leakage of liquid when the microwell was ﬁlled with cell suspension. This was evident when anhydrous copper sulfate was dispensed around the ﬁlled microwell, in a regulated environment, did not cause any change in color, i.e., from its natural white to blue color.

3.2. Cell Pretreatment The DEP suspending medium (dextrose solution) was prepared and characterized as described in our previous article [38]. The prepared 100 mL suspending medium was divided into five separate beakers. Into each beaker, except the first, calculated volume of phosphate buffer saline (PBS) was added to successively change the conductivity of the DEP suspending medium to obtain the following conductivities (in mS/m): 50, 60, 74, 88 and 97. Female normal peripheral mononuclear cells (PBMCs) Micromachines 2020, 11, 340 6 of 19 and infiltrating ductal adenocarcinoma cells (ADCs) with no identifiable angiolymphatic invasion were obtained from Conversant Bio, Huntsville, AL, USA. Also, the cells obtained did not have any identifiable information about the patient itself except their gender and age (Institutional Review Board - IRB exempt). The cells were prepared for experiment according to the supplier’s instructions. Thereafter, a known number of cells were transferred into each of the five DEP suspending medium solution where they were washed twice and diluted in 1:400 cell: suspending medium ratio before being pipetted into the DEP microwell for experiment.

3.3. Measurement of Crossover Frequency After the assurance that the microwell was leakage-free, the platinum electrodes were connected to the two terminals of an 80 MHz Siglent SDG 2082X Arbitrary Waveform Generator (Siglent Technologies, Solon, OH, USA), which supplied an 8 V peak-to-peak sinusoidal AC signal of shifting frequencies. 5 µL of the PBMCs suspension prepared as discussed in Section 3.2 was transferred into the microwell and allowed to equilibrate. Then, about 4 µL was carefully siphoned from the well so that fewer cells (between 4–7 cells) were present in the field-of-view for the experiment. Having fewer cells does not only reduce the influence of particle-particle interaction, but also enhances clarity in visualizing cells for crossover frequency determination. The waveform generator was then switched on to generate electric field gradient around the electrodes. Movement of cells was monitored and captured with a high-speed camera at 30 fps as a function of the changing field frequency until the crossover frequency was found. There was no movement of cells or flow when the waveform generator was turned off. The experiment was repeated four times (technical replicates) and there were two set of biological replicates obtained for the experiments and the crossover frequency was found in each case. More experiments were run using the other modified medium at varying conductivities thus obtaining crossover frequency spectra. The PBMCs are majorly lymphocytes (>80%) ~10 µm in diameter while ADCs are ~20 µm in diameter. Measurements were made at room temperature conditions, i.e., T = 24 1 C. ± ◦ 4. Finite Element Modeling and Simulation In this section, attention was given to the numerical modelling and simulation performed using the dielectric properties obtained from the crossover frequency measurements in Section 3.3. COMSOL Multiphysics 5.3a (Comsol Inc., Stockholm, Sweden) was used to solve fluid flow, electrostatics, and particle tracing modules in an integrated stationary and time-dependent fashion. The architecture of the separation device (Figure2) was arrived at after a series of parameter modification that ensured a complete separation of ADCs from its mixture with PBMCs. The design was made in 2D because the width to depth ratio was more than 5:1. Electric current mode was used to solve, in steady states, the current conservation equation based on Ohms law and electric displacement relations using the electric potential as the dependent variable. This was solved in steady state because the charge relaxation time for the conducting media (water, in this case 3.6 10 6 s) is less than the external time scale for device operation (10 s). Solving this × − Ohm’s law with the charge conservation and electric displacement equations gives the electric field, E, which was used to compute the electroosmotic boundary condition used in the creeping flow analysis according to uEO = µEOE, where uEO is the electroosmotic velocity- the velocity of the bulk of the fluid flowing in the channel due to electric field effects. In the incompressible creeping flow analysis (as is the usual case in microfluidic channel where the Reynolds number is significantly less than unity and viscous force is dominant), the steady state form Stokes equation together with the continuity equation was solved as the synergistic conservation of momentum and mass, which account for the velocity profile within the fluidic channel. The magnitude of this velocity as a function of the position within the channel was then used to solve the drag force (Table1) acting on the particles flowing within the channel through numerical coupling. The drag force is then counterbalanced by the dielectrophoretic force, Equation (5), at the region where the magnitude of electric field norm was modified as a Micromachines 2020, 11, x 6 of 19 suspending medium solution where they were washed twice and diluted in 1:400 cell: suspending medium ratio before being pipetted into the DEP microwell for experiment.

3.3. Measurement of Crossover Frequency: After the assurance that the microwell was leakage-free, the platinum electrodes were connected to the two terminals of an 80 MHz Siglent SDG 2082X Arbitrary Waveform Generator (Siglent Technologies, Solon, OH, USA), which supplied an 8 V peak-to-peak sinusoidal AC signal of shifting frequencies. 5 µL of the PBMCs suspension prepared as discussed in Section 3.2 was transferred into the microwellMicromachines and2020 ,allowed11, 340 to equilibrate. Then, about 4 µL was carefully siphoned from the7 ofwell 19 so that fewer cells (between 4–7 cells) were present in the field-of-view for the experiment. Having fewer cells does not only reduce the influence of particle-particle interaction, but also enhances clarity in result of the constrictions placed between the inlet and the outlet channels. Each particle moving visualizing cells for crossover frequency determination. The waveform generator was then switched through the microdevice was tracked using the particle tracing module solved in time-dependent on tomode. generate Tracking electric the particlesfield gradient enabled around the statistics the electrodes. through which Movement the device of parameters cells was (likemonitored voltage, and captureddevice with dimensions, a high-speed etc.) thatcamera generated at 30 fps the desiredas a function separation of the of changing the particles field were frequency noted. Using until the crossovera free triangular frequency customized was found. mesh, There with was diff erent no movement sizes, growth of rate, cells and or curvature flow when factor the for waveform both generatorconstrictions was turned and the off. remaining The experiment regions within was therepeated channel, four the geometrytimes (technical was discretized replicates) and and made there wereready two set for finiteof biological element analysis.replicates Multifrontal obtained for massively the experiments parallel (MUMPS) and the solver,crossover which frequency performs was foundGaussian in each factorization, case. More was experiments used in the stationary were run mode using to obtain the other the velocity modified profile medium and the electricat varying conductivitiesfield norms. thus MUMPS obtaining solved crossover for the velocity frequency profile andspectra. the electric The PBMCs field norms are these majorly values lymphocytes with a (>80%)relative ~10 µm tolerance in diameter of 0.001 while and without ADCs any are recourse~20 µm toin lumping diameter. while Measurement computing thes w fluxes.ere made GMRES at room temperature(generalized conditions minimal, residuali.e., T = 24 solver), ± 1 °C. a solver that approximates solutions by the vector in a Krylov subspace with minimal residual, was used in the transient domain to track the particles with respect to their position in space and velocity magnitude as a function of time. The final geometry of the 4. Finite Element Modeling and Simulation device where complete separation occurs was 1.4 mm in length with 5 semi-circular constriction of radiusIn this 0.1 section, mm and attention inter-structural was given constriction to the numerical spacing of modelling 85 µm. The and distance simulationD (Figure performed2) between using the dielectricthe constriction properties end and obtained the upper from channel the wall crossover was fixed fre toquency be 35 µ m. measurements This distance forbidsin Section two 3.3. COMSOLcancer cells Multiphysics to pass through 5.3a the(Comsol separation Inc region., Stockholm at any given, Sweden time. This) was design used was to made solve to prevent fluid flow, electrostatics,any form ofand shielding particle that tracing may eventuallymodules in result an integrated in incomplete stationary separation. and Table time1 provides-dependent a list fashion. of parameters, variables, boundary conditions in each type of study utilized in COMSOL, and equations The architecture of the separation device (Figure 2) was arrived at after a series of parameter associated with the modeling and simulation. Zeta potential for PDMS was assumed to be 0.1 V and modification that ensured a complete separation of ADCs from its mixture with PBMCs.− The design a relative permittivity of 80 was used in the simulation. The flow velocity at the inlet was assumed to was madebe 0.001 in m 2D/s. because the width to depth ratio was more than 5:1.

Figure 2. Optimal device design geometry obtained by COMSOL modeling and simulation utilizing Figure 2. Optimal device design geometry obtained by COMSOL modeling and simulation utilizing the electrophysiological properties of PBMCs and ADCs from the PDMS microwell. Entire microﬂuidic the electrophysiological properties of PBMCs and ADCs from the PDMS microwell. Entire platform is ~1.5 mm with semi-circular constrictions embedded in the channel. Inlet channel is 125 microfluidicµm wide platformand the two is outlet ~1.5 mmchannel with widths semi are-circular ~62.5 µ m. constrictions Pt electrodes embedded in the inlet andin the outlet channel. ports is Inlet connected to a DC power supply to further sort ADCs from healthy PBMCs.

Micromachines 2020, 11, 340 8 of 19

Table 1. List of parameters, variables, discretization, type of study utilized, and the equations associated that was incorporated into COMSOL package for optimizing the device geometry and sorting of adenocarcinoma (ADCs) from healthy peripheral blood mononuclear cells (PBMCs).

Dependent Physics/Parameters Tag Discretization Study Equation Variable

J = Qj v ∇· · J = σE + J Lagrange e Electric current ec V Stationary E = V Quadratic −∇ Wall boundary- insulated (n J = 0) h · i pI + µ( u + ( u)T + ∇· − ∇ ∇ F = 0 ρ (u) = 0 Fluid Flow spf u P2 + P1 Stationary ∇· Wall boundary- electroosmosis u = µeoEt r0 µeo = ξ; Et = E (E n)n ∀ µ − ·

Formulation d(mpv) dt = Ft F = 1 m (u v) D τp p 2 − Newtonian ρpdp τp = 18µ Particle tracing ptf q, v Transient FDEP = 2πr3 real( )real(K) E 2 p 0 r∗ ∇| | Drag law ∗ ∗ r,p− r K = + r∗ = r in r∗,p 2r∗ ∀ stationary ﬁeld Stokes Wall boundary- particles bounce-oﬀ walls Calibration Mesh Type Max size Boundary layer transition Meshing Smooth transition to Fluid dynamics Free triangular 0.001 mm interior mesh Stationary solver MUMPS Transient Solver GMRES

5. Results and Discussion In this section, we ﬁnally discuss and present the important results to prove that breast cancer can be detected early enough using whole blood. This simulation study demonstrating sorting of ADCs from PBMCs will further be validated experimentally (beyond the scope of this article). Our results are categorized into sections demonstrating: (1) experimental evidence of electrophysiological characterization of both healthy PBMCs and breast cancer ADCs, (2) validation of our microwell technique by comparing with studies from literature and (3) modeling and simulation parameters like meshing, stationary analysis, transient analysis.

5.1. Electrophysiological Characterization of PBMCs and ADCs Experimentally In estimating the properties of both PBMCs and ADCs movement of cells toward or away from high field region was tracked until the crossover frequencies were found in case at changing properties of the suspending medium. Figure3A,B shows an ADC cell experiencing positive and negative DEP force (pDEP and nDEP) respectively. In Figure3C,D, we manually tracked the movement of the target cell as previously demonstrated for prostate cancer in Hele-Shaw flow cell by Huang et al. [39]. Figure3E shows the first crossover frequency behavior when cells experience a switch from nDEP to pDEP. This first crossover frequency, usually in Hz–kHz range is mainly due to the membrane associated proteins, shape, and size of the cell. The first crossover frequency is often enough to study the phenotype of the cells; however, to characterize their genotype, the 2nd crossover frequency value has to be obtained, often in MHz range. Micromachines 2020, 11, 340 9 of 19 Micromachines 2020, 11, x 9 of 19

(E)

Figure 3.3. ADCADC cellscells experiencing experiencing DEP DEP in in the the microwell microwell at varyingat varying AC frequencies-AC frequencies (A)- shows (A) shows the ADC the cellsADC experiencingcells experiencing positive positive DEP (pDEP)DEP (pDEP) wherein wherein the cells the cells move move towards towards the high-fieldthe high-field region region or the or triangularthe triangular electrode electrode in here in here and and (B) shows(B) shows the ADCthe ADC cells cells experiencing experiencing nDEP nDEP behavior behavior wherein wherein the cellsthe cells move move away away from from the highthe high field field region. region. (C,D ()C are) and the ( imagesD) are the resulting images from resulting manual from tracking manual of thetracking target of cell the (labeled target Tg) cell as (labeled demonstrated Tg) as demonstratedin [39]. (E) shows in [ a39 plot]. ( ofE) real shows part a of plot Clausius-Mossotti of real part of factorClausius varying-Mossotti with factor frequency varying (Hz). with Here frequency the cells (Hz). initially Here experience the cells nDEP initially (negative experience DEP) nDEP and as(negative the frequency DEP) and increases, as the frequency they switch increases, to pDEP they (positive switch DEP)to pDEP where (positive the switch DEP) iswhere termed the asswitch first crossoveris termed as frequency. first crossover frequency.

The crossover frequency data for PBMCs and ADCs were fittedfitted using Equation (1).(1). This equation is an ideal model owing to the spherical nature of lymphocytes. Eq Equationuation (1)(1) is also suitable for ADCs even though they are a a little little distorted. distorted. Kirby and Huang et al. al. had reported that an isotopically inhomogeneous non non-spherical-spherical cell cell can still be analyzed, to a good approximation, with single shell model since the spherical harmonic solutionssolutions used in thethe eigenfunctioneigenfunction expansionexpansion approximationsapproximations for DEP force force can can help help define define the the e effectiveffective particle particle propertiesproperties [[3939,40,40].]. Since the second crossover frequencies couldcould notnot bebe obtainedobtained due due to to the the limitation limitation of of the the measuring measuring equipment, equipment, often often obtained obtained at at high frequency range (>50 MHz), the cytoplasmic properties used in the simulation were as reported by Qiao et al. using impedance measurement [41]. The total (effective) particle conductivity,

Micromachines 2020, 11, 340 10 of 19 high frequency range (>50 MHz), the cytoplasmic properties used in the simulation were as reported by Qiao et al. using impedance measurement [41]. The total (eﬀective) particle conductivity, σ_p, and permittivity was obtained as described by Adekanmbi et al. [3] and Pethig [31] respectively. Table2 provides the dielectric properties obtained from our experiments that are compared to the other published literature values in case of PBMCs. It should be noted that the conductivity of the infected ADCs rise sharply compared to the healthy PBMCs that may be attributed to the introduction of new membrane permeation pathways, to membrane peroxidation damage, and to changes in membrane ﬂuidity following infection [42].

Table 2. Dielectric properties, i.e., conductivity and permittivity obtained from our novel electrokinetic technique based on cell response obtained at crossover frequency for ADCs and healthy PBMCs using an osmotic concentration suspending medium maintained at osmotic conductivity and permittivity. Literature reported values has been compared with our novel technique for PBMCs only as a measure of validation [43].

ADCs (Inﬁltrating Ductal PBMCs (Lymphocytes) Adenocarcinoma Cells) Property Suspending Crossover Freq. Crossover Freq. Literature Medium Technique Technique Reported [43] Conductivity (S/m) 1.3 0.67 0.66 0.055 Permittivity 69 62 59.62 80

The data fitted using MATLAB in Figure3E were analyzed using chi-square test. The expected value of the crossover frequency is determined from the curves in Figure3E at Re (K(w)) = 0 to prove that the fitting is reasonable. The χ2 critical value at 0.05 significance value is obtained to be 11.07. The χ2 test statistic value for ADCs and PBMCs are found to be 1.1804 and 2.413 respectively. Since, the calculated test statistic is less than the critical χ2 value, it signifies a reasonably good fit, i.e., there is no significant difference between the observed (curve) and expected (experimental) values. However, the authors believe that this is the first time that ADCs were characterized using a novel electrokinetic technique to obtain their dielectric properties i.e., permittivity and conductivity as shown in Table2.

5.2. Parameters Affecting COMSOL Modeling and Simulation to Obtain High Sorting Efficiencies In this section, we discuss the factors that affect the optimization of the device geometry to achieve high sorting efficiencies that further influence early breast cancer detection obtained through sorting ADCs from healthy PBMCs.

5.2.1. Meshing of the Device Design in COMSOL Meshing is one of the factors that strongly affect modelling requirements. Choosing the right mesh element types and sizes is highly pivotal to the accuracy of the simulation results in any finite element problem. Under-meshing can result in solutions that are far less than accurate while over meshing can result in large amount of computational time due to the mesh using too many unnecessary elements. To prevent under meshing, we used mesh elements greater than 40,000. Over meshing was, however, checked and prevented by using meshing sequence with local and global attributes. The local mesh density at the constrictions was sufficiently increased by reducing mesh size while the remaining part of the geometry (where dielectrophoretic force would not have significant effects) was meshed at increased mesh size. This meshing sequence, which was based on Lagrange quadratic representation, reduced the total number of mesh element by 45.17% and computation period by 51.06%. Since the dielectrophoretic force, which causes cells to separate based on their movement away or towards the high field region, acts significantly at the channel constriction zone, it was necessary to verify if the maximum element size (MES) at the constriction would affect the transmission probability of ADCs Micromachines 2020, 11, 340 11 of 19

Micromachines 2020, 11, x 11 of 19 and to what extent would that effect be. As shown in Figure4, the accuracy of the solution (which is a in Figure 4, the accuracy of the solution (which is a function of the transmission probability) depends function of the transmission probability) depends on the choice of mesh size. The mesh characteristics on the choice of mesh size. The mesh characteristics that was found to be optimum at the applied that was found to be optimum at the applied effective potential difference is as given in Table1. effective potential difference is as given in Table 1.

Figure 4. The discretization of the separation region,region, i.e.,i.e., along the semicircularsemicircular constrictions where maximum DEP DEP e ﬀ effectect is observedis observed that that causes causes the cells the to cells move to into move categorized into categorized streamlines streamlines by adopting by variableadopting mesh variable element mesh size element (MES). size (MES).

FigureFigure4 4 demonstrates demonstrates thethe gradationgradation ofof thethe discretizationdiscretization regimeregime ofof thethe constrictionconstriction zonezone asas thethe maximum element element size size (MES) (MES) is progressively is progressively reduced. reduced. At MES At = MES0.05 mm= 0.05 the mm density the of density the triangular of the meshtriangular is very mesh low is indicating very low thatindicating the inter-nodal that the inter distance-nodal within distance the discretizedwithin the discretized zone is large. zone This is largelarge. distanceThis large depicts distance an depicts inefficient an ineffici solutionent capacity solution for capacity the gradient for the ofgradient the electric of the field, electric which field, is evidentwhich is in evident the low in transmission the low transmission probability pro (TP)bability for the (TP) ADCs for (Figure the ADCs5). Transmission (Figure 5). Transmission Probability, TP,Probability, is referred TP, to is as referred the ratio to of as the the number ratio of of the particles number at of a specifiedparticles exitat a tospecified the total exit number to the of total the particlesnumber of at the particles inlet. In otherat the words, inlet. In large other mesh words, size large at the mesh constriction size at the zone constriction was not able zone to correctlywas not solveable to for correctly the electric solve field for the gradient electric which field isgradient necessary which for dielectrophoreticis necessary for dielectrophoretic influence on the influence particles. Whenon the theparticles. mesh sizeWhen was the progressively mesh size wa reduced,s progressively the number reduced, of elements the number increased of elements correspondingly. increased Thiscorrespondingly. in turn increased This thein turn separation increased effi ciencythe separation at the constriction efficiency at zone, the henceconstriction the dramatic zone, hence ramping the updramatic of the ramping percentage up ofof ADCsthe percentage that were of sorted ADCs fromthat were healthy sorted PBMCs. from healthy It is important PBMCs. to It noteis importa that thent progressiveto note thatreduction the progressive in MES reductionincreases the in computation MES increases time, the i.e., computation with MES at time 0.0005, i.e. mm, with and MES 0.0001 at mm0.0005 requiring mm and 800% 0.0001 and mm 960% requiring more time800% than and at960% 0.001 more mm. time Since than the at TP 0.001 value mm. for Since MES the= 0.001 TP value mm, 0.0005for MES mm = 0.001 and mm, 0.0001 0.0005 mm aremm comparatively and 0.0001 mm similar are comparatively and >97%, the similar computation and >97%, was the carried computation out at 0.001was carried mm with out anat 0.001 error mm margin with of an ~< error0.00020%. margin At of these ~ <0.00020%. values (0.001, At these 0.0005 values and (0.001, 0.0001 0.0005 mm), and it is safe0.0001 to concludemm), it is that safe the to stationaryconclude that and transientthe stationary solutions and (withintransient the solutions marginof (within error) ofthe the margin coupled of physicserror) of do the not couple vary withd physics mesh condition do not vary as the with TP values mesh condition tend to be asapproximately the TP values constant. tend to MES be valueapproximately beyond 0.0001 constant. mm showed MES value critical beyond error warning0.0001 mm sign showed in COMSOL critical and error was warning computationally sign in veryCOMSOL expensive. and was computationally very expensive.

Micromachines 2020, 11, 340 12 of 19 Micromachines 2020, 11, x 12 of 19

FigureFigure 5. 5.Transmission Transmission probability probability of ADCs of ADCs as a function as a function of themaximum of the maximum element size element at the separationsize at the zone,separation i.e., around zone, thei.e., semicirculararound the semicircular constriction constriction region. Since region. MES atSince 0.001 MES mm, at 0.0005 0.001 mm, 0.0005 and 0.0001 mm, mmand are0.0001 almost mm similar, are almost the simulationsimilar, the was simulation completed was ﬁxing completed MES atfixing 0.001 MES mm. at 0.001 mm.

5.2.2.5.2.2. StationaryStationary FieldField AnalysisAnalysis TheThe numericalnumerical computationcomputation comprisescomprises of of two two stationary stationary fields: fields: (a) a) creepingcreeping (fluid)(fluid) flowflow and and (b) b) electricelectric current current (ec). (ec). The The electric electric current current was was solved solved in thein the stationary stationary mode mode to generate to generate the electric the electric field thatfield not that only not generated only generated the electro-osmotic the electro- eosmoticffects at theeffects channel at the wall channel but also wall provided but also the provided distribution the ofdistribution field strength, of field E, whose strength, gradient E, whose provided gradient the provided necessary the dielectrophoretic necessary dielectrophoretic force at the constrictions. force at the constrictions.As shown in Figure6A, when DC potential di fference was applied across the channel (from the inlet toAs outlet) shown and in Figure there was6A, awhen distribution DC potential of the difference electric field was as applied governed across by thethe Laplacechannel equation.(from the Theinlet tips to outlet) of the constrictionsand there was within a distribution the channel, of the generated electric field thehighest as governed field strengthby the Laplace region equation. that was importantThe tips of for the dielectrophoretic constrictions within separation. the channel, In Figure generated6, the e theffect highest of the fieldfield gradient strengthis region visually that more was pronouncedimportant for when diele thectrophoretic flow field separation. lines were In plotted Figure together 6, the effect with of the the electric field gradient field norm. is visually Glaringly, more thepronounced gradient ofwhen the fieldthe flow which field was lines utilized were by plotted the dielectrophoretic together with the force electric acting field at thenorm. constrictions Glaringly, interferethe gradient with of the the velocity field which field. Thewas dielectrophoretic utilized by the dielectrophoretic velocity introduced force at theacting constrictions at the constrictions added to theinterfere already with existing the velocity electrophoretic field. The and dielectrophoretic electroosmotic velocity velocities introduced apart from at thethe increaseconstrictions in velocity added thatto the was already introduced existing by electrophoretic the continuity equationand electroosmotic owing to the velocities reduction apart in from flow area.the increase Figure6 inC velocity shows thethat ripple was eff introducedects generated by from the the continuity surface of equation the constrictions owing to outwards. the reduction The resultant in flow effects area. of thisFigure streamline 6C shows interference the ripple could effects be seengenerated in Figure from6D–F the at surface varying of DC the voltage, constrictions i.e., 10 outwards. V, 110 V, and The 60resultant V respectively. effects of The this number streamline of constrictions interference werecould fixed be seen at 5 in and Figure diameter 6D, E, of theand constrictionF at varying was DC consideredvoltage, i.e. to, 10 be V, 100 110µm. V, and 60 V respectively. The number of constrictions were fixed at 5 and diameterEffects of of the applied constriction potentials was andconsidered constriction to be radius100 μm. on transmission probability: It is important to verify the effects of the electric field strength at various applied potentials and constrictions on the separation efficiency of the microdevice platform. As a result, the radius of the constrictions was varied keeping the number (#) of constrictions fixed at 5 at a given time thus resolving the Laplace equation each time using different applied potential without varying the mesh conditions (Figure7). The number of constrictions was fixed as an optimization test constraint with respect to the length of the device as well as the exploration of the possibility of initiating cellular separation with minimal insulating constrictions as previously demonstrated by Adekanmbi et al. [38].

(A) (B) (C)

Micromachines 2020, 11, x 12 of 19

Figure 5. Transmission probability of ADCs as a function of the maximum element size at the separation zone, i.e., around the semicircular constriction region. Since MES at 0.001 mm, 0.0005 mm, and 0.0001 mm are almost similar, the simulation was completed fixing MES at 0.001 mm.

5.2.2. Stationary Field Analysis The numerical computation comprises of two stationary fields: a) creeping (fluid) flow and b) electric current (ec). The electric current was solved in the stationary mode to generate the electric field that not only generated the electro-osmotic effects at the channel wall but also provided the distribution of field strength, E, whose gradient provided the necessary dielectrophoretic force at the constrictions. As shown in Figure 6A, when DC potential difference was applied across the channel (from the inlet to outlet) and there was a distribution of the electric field as governed by the Laplace equation. The tips of the constrictions within the channel, generated the highest field strength region that was important for dielectrophoretic separation. In Figure 6, the effect of the field gradient is visually more pronounced when the flow field lines were plotted together with the electric field norm. Glaringly, the gradient of the field which was utilized by the dielectrophoretic force acting at the constrictions interfere with the velocity field. The dielectrophoretic velocity introduced at the constrictions added to the already existing electrophoretic and electroosmotic velocities apart from the increase in velocity that was introduced by the continuity equation owing to the reduction in flow area. Figure 6C shows the ripple effects generated from the surface of the constrictions outwards. The resultant effects of this streamline interference could be seen in Figure 6D, E, and F at varying DC voltageMicromachines, i.e.,2020 10 ,V,11 ,110 340 V, and 60 V respectively. The number of constrictions were fixed at 5 13and of 19 diameter of the constriction was considered to be 100 μm.

Micromachines 2020, 11, x 13 of 19 (A) (B) (C)

(D) (E) (F)

FigureFigure 6. 6. FieldField and and velocity velocity profiles profiles obtained obtained from from solving solving the the electrostatics electrostatics and and stokes stokes equations equations in in stationarystationary mode. mode. (A (A) )is is the the electric electric field field norm, norm, (B (B) is) is the the combination combination of ofthe the field field norm norm with with velocity velocity streamlines,streamlines, ((CC)) isis the the zoomed zoomed image image showing showing the e theffect effect of the ofconstriction the constriction zone on zonevelocity on streamlines. velocity streamlines.(D–F) show ( streamlinesD–F) show based streamlines on changing based on DC changing voltage at DC 10 voltageV, 110 V at and 10 60 V, V 110 respectively. V and 60 VThe Micromachines 2020, 11, x 14 of 19 respectively.constriction diameterThe constriction and number diameter were and fixed number to be were 100 µ fixedm and to 5 be respectively. 100 μm and 5 respectively.

Effects of applied potentials and constriction radius on transmission probability: It is important to verify the effects of the electric field strength at various applied potentials and constrictions on the separation efficiency of the microdevice platform. As a result, the radius of the constrictions was varied keeping the number (#) of constrictions fixed at 5 at a given time thus resolving the Laplace equation each time using different applied potential without varying the mesh conditions (Figure 7). The number of constrictions was fixed as an optimization test constraint with respect to the length of the device as well as the exploration of the possibility of initiating cellular separation with minimal insulating constrictions as previously demonstrated by Adekanmbi et al. [38]. Transmission probability of the total number of PBMCs (from inlet to outlet) as a function of the constriction gap, i.e., D in Figure 2 and applied voltage using a fixed number of constriction entities, i.e., 5 was calculated and plotted as shown in Figure 7. Transmission probability (TP) is congruent to normalizing the amount of PBMCs recovered by the initial amount of PBMCs in the inlet mixture. This means, a TP value of 1 represents 100% separation of the PBMCs from its mixture with ADCs. The essence of calculating the transmission probability was to verify the selectivity of the device and FigureFigure 7.7. EEffectsffects ofof constrictionconstriction clearanceclearance // size,size, i.e.,i.e., diameterdiameter andand DCDC voltagevoltage onon thethe transmissiontransmission to track operating parameters that would be optimal for the operability of the device. Figure 7 probabilityprobability ofof ADCs.ADCs. DiameterDiameter ofof thethe constrictionsconstrictions werewere varied—80,varied—80, 90,90, 100,100, andand 110110µ μmm keepingkeeping thethe demonstrates the effect of varying the constriction diameter and the applied voltage on the numbernumber (#)(#) ofof constrictionsconstrictions fixed,fixed,i.e., i.e.,5 5at at a a given given time. time. PerfectPerfect sortingsorting waswas observedobserved forfor constrictionconstriction transmissiondiameter of probability 100 µm at voltages of PBMCs.>50 V The. TP value for each of the constriction diameter was diameter of 100 μm at voltages >50 VDCDC. progressively increased with the changing potential. At a given DC voltage, the recovery of PBMCs was highestTransmission when probability the constriction of the diameter total number was of 100 PBMCs μm. More (from so, inlet from to outlet) 50 V toas a80 function V, 100 ofμm the Since increasing electric potential could result in increased Joule heating of the microdevice constriction diameter gap, i.e., Dgave in Figurea perfect2 and separation applied voltageof the PBMCs. using a fixedNone numberof the constriction of constriction diameters entities, leading to unwholesome modification of the electrokinetic and dielectrophoretic effects, 100 μm gavei.e., 5 100% was calculatedseparation and except plotted 110 μ asm shown at 80 V. in These Figure variations7. Transmission in transmission probability probability (TP) is congruent could be to constriction diameter was considered to be the ideal dimension for the separation device platform. attributednormalizing to thethe amountchanging of ele PBMCsctric field recovered strengths by the as initial the applied amount voltage of PBMCs and inconstriction the inlet mixture. diameter This Furthermore, operating at a lower voltage, i.e., ~60 VDC seems to reduce the risk of Joule heating change.means, aChanging TP value the of 1applied represents DC 100%potential separation affected ofthe the electrokinetic PBMCs from and its dielectrophoretic mixture with ADCs. forces The within the insulator-based dielectrophoretic device. operatingessence of calculatingwithin the the channel. transmission Electrokinetic probability contributions was to verify within the selectivity the channel of the affects device the and particle to track velocity and hence the resident time within which the particles are expected to experience strongest operating5.2.3. Transient parameters Analysis that would be optimal for the operability of the device. Figure7 demonstrates DEPthe e ffforceect of at varying the constriction the constriction zone. At diameter <50 V, the and electro the applied-osmotic voltage velocity on theof the transmission bulk fluid probabilitymedium was lowParticle enough tracking to move analysis the particles was used slowl toy trace to the the constriction movement zone of both where ADCs there and is ample PBMCs residence along the timewhole for microdevice the cells to experience platform. Theresufficient is no induced change dielectrophoretic observed in the particles’ force that trajectory would cause when them the toparticle be separatedposition isadequately. placed either However, at the centersince DEP or the force edge depends of the oninlet square, since of a the uniform field gr particleadient, distributionthe low DC is potentialselected in(< 50COMSOL V) could withi not ngenerate the channel. the required There is electric no surface field interaction gradient that with is the sufficient particles to dueinduce to the strong“bounce negative-off” condition dielectrophoretic selected forcein COMSOL. necessary Particles for sorting were the seen cells movinginto their through respective the differential channel inlet outlets.until they were acted upon by the dielectrophoretic force at the constriction which tend to move the particles either towards or away from the constriction surface depending on the properties of the medium, ADCs, PBMCs, and the generated electric field gradient. From the equation of the dielectrophoretic force (Equation (5)), the force experienced by both PBMCs and ADCs at the constriction depends on the square of the electric field gradient as well as the radius of the particle to the third power. The membrane conductivity of both ADCs and PBMCs are both less than that of the medium. Therefore, it is expected that both of them would experience negative DEP. Figure 8 demonstrates the scenario where ACDs and PBMCs were partially and completely separated while shifting the applied voltage for a constriction number of 5 and diameter of 100 µm at fixed medium properties. Figure 8A depicts incomplete separation at DC voltage below 50 V. At this applied voltage the strength of the applied electric field was not sufficient enough to push away the PBMCs. At 50 V, the generated field gradient had made the DEP force more negative such that the PBMCs were pushed away enough from the high field region to cause their separation from ADCs (Figure 8B). No separation was observed at higher DC voltages, i.e., >100 V (Figure 8C). However, there was separation at ~100 V but with some interesting modification to the flow streamlines as shown in Figure 9.

Micromachines 2020, 11, 340 14 of 19 of PBMCs. The TP value for each of the constriction diameter was progressively increased with the changing potential. At a given DC voltage, the recovery of PBMCs was highest when the constriction diameter was 100 µm. More so, from 50 V to 80 V, 100 µm constriction diameter gave a perfect separation of the PBMCs. None of the constriction diameters gave 100% separation except 110 µm at 80 V. These variations in transmission probability could be attributed to the changing electric field strengths as the applied voltage and constriction diameter change. Changing the applied DC potential affected the electrokinetic and dielectrophoretic forces operating within the channel. Electrokinetic contributions within the channel affects the particle velocity and hence the resident time within which the particles are expected to experience strongest DEP force at the constriction zone. At <50 V, the electro-osmotic velocity of the bulk fluid medium was low enough to move the particles slowly to the constriction zone where there is ample residence time for the cells to experience sufficient induced dielectrophoretic force that would cause them to be separated adequately. However, since DEP force depends on square of the field gradient, the low DC potential (<50 V) could not generate the required electric field gradient that is sufficient to induce strong negative dielectrophoretic force necessary for sorting the cells into their respective differential outlets. Since increasing electric potential could result in increased Joule heating of the microdevice leading to unwholesome modification of the electrokinetic and dielectrophoretic effects, 100 µm constriction diameter was considered to be the ideal dimension for the separation device platform. Furthermore, operating at a lower voltage, i.e., ~60 VDC seems to reduce the risk of Joule heating within the insulator-based dielectrophoretic device.

5.2.3. Transient Analysis Particle tracking analysis was used to trace the movement of both ADCs and PBMCs along the whole microdevice platform. There is no change observed in the particles’ trajectory when the particle position is placed either at the center or the edge of the inlet, since a uniform particle distribution is selected in COMSOL within the channel. There is no surface interaction with the particles due to the “bounce-off” condition selected in COMSOL. Particles were seen moving through the channel inlet until they were acted upon by the dielectrophoretic force at the constriction which tend to move the particles either towards or away from the constriction surface depending on the properties of the medium, ADCs, PBMCs, and the generated electric field gradient. From the equation of the dielectrophoretic force (Equation (5)), the force experienced by both PBMCs and ADCs at the constriction depends on the square of the electric field gradient as well as the radius of the particle to the third power. The membrane conductivity of both ADCs and PBMCs are both less than that of the medium. Therefore, it is expected that both of them would experience negative DEP. Figure8 demonstrates the scenario where ACDs and PBMCs were partially and completely separated while shifting the applied voltage for a constriction number of 5 and diameter of 100 µm at fixed medium properties. Figure8A depicts incomplete separation at DC voltage below 50 V. At this applied voltage the strength of the applied electric field was not sufficient enough to push away the PBMCs. At 50 V, the generated field gradient had made the DEP force more negative such that the PBMCs were pushed away enough from the high field region to cause their separation from ADCs (Figure8B). No separation was observed at higher DC voltages, i.e., >100 V (Figure8C). However, there was separation at ~100 V but with some interesting modification to the flow streamlines as shown in Figure9. Micromachines 2020, 11, x 15 of 19

Micromachines 2020, 11, 340 15 of 19 Micromachines 2020, 11, x 15 of 19

(A) (B) (C)

Figure 8. Particle trajectories showing partial (A,C) and complete separation (B) at various voltage conditions. The constriction diameter was fixed at 100 µm along with number of constrictions at 5. (A) shows incomplete separation at <50 VDC, (B) complete separation at 50 VDC, (C) no separation at >100 VDC.

In Figure 9A, the operating DC voltage is 60 V while Figure 9B is at 100 V. At 120 V (Figure 9C), some streamlines are being recirculated and this recirculation became more and more pronounced as

the applied voltage increased to 200 V (Figure 9D–F). Figure 9D shows the close-up section of the bifurcation zone(A at) 200 V, where in more recirculation(B) of streamlines are being observed.(C) Figure 9E is a close-up representation of the streamline recirculation showing some of the cells that were forced Figure 8. Particle trajectories showing partial ( A,C) and complete separation ((B)B) at various voltage to moveconditions. in a circular The The constriction constriction reverse direction diameter diameter towaswas the fixed ﬁxedDEP at force. at100 100 µm Asµ malong shown along with within number Figure number of9F, constrictions ofsome constrictions of the at cells 5. at(A 5.that) were heading towards the exit ports are also forced to move towards the inlet, i.e., recirculated back (showsA) shows incomplete incomplete separation separation at <50 at 100 at into the main channel. >V100DC. VDC.

In Figure 9A, the operating DC voltage is 60 V while Figure 9B is at 100 V. At 120 V (Figure 9C), some streamlines are being recirculated and this recirculation became more and more pronounced as the applied voltage increased to 200 V (Figure 9D–F). Figure 9D shows the close-up section of the bifurcation zone at 200 V, where in more recirculation of streamlines are being observed. Figure 9E is a close-up representation of the streamline recirculation showing some of the cells that were forced to move in a circular reverse direction to the DEP force. As shown in Figure 9F, some of the cells that were heading towards the exit ports are also forced to move towards the inlet, i.e., recirculated back into the main channel. (A) (B) (C)

((AD)) ((EB)) (F()C )

FigureFigure 9. 9.Velocity Velocity streamlines streamlines at various at various applied applied DC voltage DC voltage conditions conditions at ﬁxed number at fixed of number constrictions of constrictions (5) and constriction size (100 µm); (A) and (B) shows streamlines at 60 VDC and 100 VDC (5) and constriction size (100 µm); (A) and (B) shows streamlines at 60 VDC and 100 VDC respectively; respectively; (C) partial recirculation observed at 120 VDC; (D) increasing recirculation at 200 VDC; (E) (C) partial recirculation observed at 120 VDC;(D) increasing recirculation at 200 VDC;(E) shows the recirculationshows the recirculation eﬀects that effects caused that non-compliant caused non-compliant behavior of behavior cells to theof cells DEP to force; the DEP and force; (F) close-up and (F) of someclose- cellsup of that some tend cells to that reach tend the to exit reach showing the exit recirculation showing recirculation as well. as well.

InThis Figure interestin9A, theg operatingdevelopment DC may voltage be associated is 60 V while with Figure the inter9B is-relation at 100 V. of At the 120 high V (Figure potentials9C), with the electric current within the channel, which, could generate a substantial amount of some streamlines are being recirculated and this recirculation became more and more pronounced astemperature the applied voltagerise that increased interferes to 200 with V (Figure the conductivity9D–F). Figure of9 D the shows fluid the-particle close-up system. section Since of the (D) (E) (F) bifurcationdielectrophoretic zone at force 200 V,is wherea function in more of conductivity recirculation of of the streamlines fluid-particle are beingsystem, observed. DEP is hampered Figure9E as is a close-up Figure representation 9. Velocity streamlines of the streamline at various recirculation applied DC showing voltage some conditions of the cells at fixed that number were forced of to moveconstrictions in a circular (5)reverse and constriction direction size to (100 the DEPµm); ( force.A) andAs (B) shownshows streamlines in Figure9 atF, 6 some0 VDC ofand the 100 cells VDC that wererespectively; heading towards (C) partial the recirculation exit ports are observed also forced at 120 to VDC move; (D) towardsincreasing the recirculation inlet, i.e., at recirculated 200 VDC; (E) back into theshows main the channel.recirculation effects that caused non-compliant behavior of cells to the DEP force; and (F) closeThis- interestingup of some cells development that tend to may reach be the associated exit showing with recirculation the inter-relation as well. of the high potentials with the electric current within the channel, which, could generate a substantial amount of temperature rise thatThis interferes interestin withg development the conductivity may ofbe theassociated ﬂuid-particle with system.the inter Since-relation dielectrophoretic of the high potentials force is a withfunction the of electric conductivity current of the within ﬂuid-particle the channel, system, which, DEP is could hampered generate as Joule a substantial heating becomes amount more of temperature rise that interferes with the conductivity of the fluid-particle system. Since dielectrophoretic force is a function of conductivity of the fluid-particle system, DEP is hampered as

Micromachines 2020, 11, x 16 of 19 Micromachines 2020, 11, 340 16 of 19 Joule heating becomes more predominant due to the increased temperature. This simulation neglected particle-particle interaction on the basis of experiments since the cell suspension were to predominant due to the increased temperature. This simulation neglected particle-particle interaction be diluted to an extent where in the cells will substantial be far apart that their interaction can be on the basis of experiments since the cell suspension were to be diluted to an extent where in the cells considered inconsequential. will substantial be far apart that their interaction can be considered inconsequential.

5.3.5.3. Validation of the DEP Microwell TechniqueTechnique TheThe electrophysiological electrophysiological properties for PBMCs PBMCs obtained data through our novel novel microwell microwell platformplatform viavia DEPDEP crossovercrossover frequency frequency measurement measurement were were validated validated by by comparing comparing the the reported reported data data in literaturein literature obtained obtained through through DEP DEP electro-rotation electro-rotation measurement measurement as as reported reported by by Chan Chan et et al. al. [ 43[44].]. TheThe samplessamples used used in in this this research research and and the the reported reported literature literature values values were fromwere non-pregnant from non-pregnant young female young (female<50 years (<50 of y age)ears since of age) pregnancy since pregnancy tends to substantially tends to substantially lower the specific lower membrane the specific conductance membrane ofconductance PBMCs [43 of]. PBMCs The electrophysiological [44]. The electrophy propertiessiological for properties PBMCs obtained for PBMCs from obtained our experiments from our andexperiments the literature and the reported literature values reported were values used towere run used the simulationto run the simulation independently independently under the under same operatingthe same conditions.operating conditions. Figure 10 shows Figure the 10 results shows of the the results comparative of the simulationcomparative where simulation a log-log where plot of a transmissionlog-log plot of probability transmission (TP) probability and the progression (TP) and timethe progression were plotted. time Statistically, were plotted. the p-value Statistically, obtained the forp-value this comparison obtained for was this 0.1 comparison (at 0.01 significance was 0.1 (at level) 0.01 implyingsignificance that level) we do implying not have that suffi wecient do evidencenot have tosufficient reject the evidence null hypothesis to reject of the “no null significant hypothesis difference” of “no between significant the two difference” outcomes. between the two outcomes.

Figure 10. Validation of the electrophysiological properties of healthy PBMCs obtained from the DEP Figure 10. Validation of the electrophysiological properties of healthy PBMCs obtained from the DEP microwell platform using crossover frequency measurement and the literature reported values based microwell platform using crossover frequency measurement and the literature reported values based on electro-rotation experiments [43]. Both the samples were derived from non-pregnant young women on electro-rotation experiments [44]. Both the samples were derived from non-pregnant young (<50 years of age). women (< 50 years of age). 6. Conclusions 6. Conclusions: Continuous dielectrophoretic separation of infiltrating ductal adenocarcinoma cells (ADCs) fromContinuous isolated peripheral dielectrophoretic blood mononuclear separation cells of infiltrating (PBMCs) using ductal direct adenocarcin currentoma in a semi-circular cells (ADCs) insulator-basedfrom isolated peripheral microchannel blood has mononuclear been numerically cells (PBMCs) studied. Theusing electrophysiological direct current in a propertiessemi-circular for PBMCsinsulator used-based in simulationsmicrochannel were has obtained been numerically in a novel studied. DEP microwell The electrophysiological platform that characterized properties thefor behaviorPBMCs used of the in cellssimulations under varying were obtained AC frequency in a novel by DEP measuring microwell the DEPplatform crossover that characterized of the cells. The the firstbehavior and secondof the cells crossover under frequency varying AC obtained frequency were by curve-fitted measuring usingthe DEP a single crossover shell modelof the cells. to obtain The thefirst conductivity and second crossover and permittivity frequency of obtained the PBMCs. were PBMCs curve-fitted vary inusing size a and single the shell sample model used to inobtain this experimentthe conductivity was majorly and permittivity small size lymphocytes,of the PBMCs. i.e., PBMCs ~10 µ mvary in diameter.in size and the sample used in this experimentDielectrophoretic was majorly force small is asize function lymphocytes of the gradient, i.e., ~10 of μ them in electric diameter. field-a factor that also depend on theDielectrophoretic applied voltage asforce well is as a function the constriction of the gradient radius. In of orderthe electric to induce field su-affi factorcient fieldthat a gradientlso depend for theon the dielectrophoretic applied voltage separation as well as of the ADCs constriction from PBMCs, radius. the In applied order to DC induce potential sufficient and the field constriction gradient for the dielectrophoretic separation of ADCs from PBMCs, the applied DC potential and the

Micromachines 2020, 11, 340 17 of 19 diameter were dynamically varied until a regime of perfect simulation was obtained at constriction diameter of 100 µm and applied DC potential of ~50 V. The number of constrictions in the channel also affects separation efficiency and 5 semi-circular constrictions lead to optimal sorting of ADCs from PBMCs. This insulator-DEP based method of separating infiltrating ductal adenocarcinoma cells (ADCs) from isolated peripheral blood mononuclear cells (PBMCs) using direct current provided a cheaper, less cumbersome, easier-to-use, and yet efficient approach when compare with previous methods that used deformability, magnetism, or dielectric affinity column. Discretization of domain (meshing) in numerical analysis is an important factor that affect the accuracy of the solution obtained from solving any associated physics within a microchannel. In this paper, effort was made to strike a balance between the computational requirements of the mesh size and the desired transmission probability. Mesh size (local and global) was carefully chosen such that the resultant solution of the simulation did not vary with meshing. To aid our understanding of the choice of applied potential and how it relates with the separation efficiency, we found out that increasing the voltage beyond 100 V DC would lead to no separation, i.e., both PBMCs and ADCs moved into one exit channel. Another interesting phenomenon was observed at higher voltages (>100 V) along with separation was recirculation behavior of cells. Some of the cells that were moving towards the exit channels were forced to change their direction back to the inlet. Recirculation increased especially between the constriction region and the bifurcation into exit channels with increasing DC potential. This behavior or wake formation is due to increased Joule heating as the temperature rises in the microfluidic platform with increasing DC potential since DEP is a function of the conductivity of the medium. This DEP spectroscopy technique based on crossover measurement allows characterizing the intracellular differences and physical properties of cells, without any labeling, without affecting cell integrity and viability. Finally, this method confirms a high potential of emerging lab-on-chip (LOC) platforms in the early diagnosis and the treatment of breast cancer especially in young women where mammography is ineffective and/or painful.

Author Contributions: Conceptualization, S.K.S.; methodology, E.O.A.; software, E.O.A. and A.T.G.; validation, E.O.A., A.T.G. and S.K.S.; formal analysis, E.O.A. and A.T.G.; investigation, E.O.A.; resources, S.K.S.; data curation, E.O.A.; writing—original draft preparation, E.O.A.; writing—review and editing, S.K.S.; visualization, S.K.S.; supervision, S.K.S.; project administration, S.K.S.; funding acquisition, S.K.S. All authors have read and agreed to the published version of the manuscript. Funding: This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. However, we would like to acknowledge the partial funding granted by Idaho IDeA Network of Biomedical Research Excellence (Idaho-INBRE) via supporting summer INBRE undergraduate fellow. Acknowledgments: We would also like to acknowledge the past undergraduate researchers Amanda Vu and Sheila Briggs for their help in DEP microwell experiments. Conflicts of Interest: The authors have declared no conflict of interest

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